first client

Hello,
I have landed my first serious project for a client who requires a new website for his company.
Specs: 10 pages with 2 contact form functionalities.
I'm fine with the design part but I am not so confident with the administrative side of things.

drawing up a contract?
budget?
request 50% of full amount before starting the project?
charge per project or per hour?
how many revisions should I offer?
anything else I should include?

Firstly, well done on getting your first project. Although I don't understand how you've won it when you haven't given them a costing?

To answer your questions you need to first roughly work out your expenses relating to your business:

Software
Heating/lighting
Equipment
Insurances
Stationery
etc etc

Then , work out how much you need to earn to pay your bills and enjoy life. From this you should start to build up a picture of how much you need to earn to live and pay your bills.

So by now you should have an idea of an hourly rate you need to earn. For example if it's £50 per hour then work out how long your project will take to complete.

Factor into this that as humans we'll underestimate the time things take by about 30%. So if you think the project will take 10 hours, it'll more than likely take 13 hours to do.

Next, multiply your hourly rate by the time the project will take, plus the extra 30%. So that would make the project cost £650 - 13 x £50.

In terms of revisions, if your brief is good and your mock-ups were spot on then revisions should be minimal, so I shouldn't worry. But if you want paying at the end of the project you need to be prepared to make some changes to meet the clients expectations.

Regarding deposit, I would get around 40-50% up front, with the balance on completion.

Make it clear in your contract that payment is due BEFORE the site goes live. Also make it clear that you will require copy and images in a timely manner, this prevents the client from drawing out the process and helps your cash flow.